The generator matrix

 1  0  0  1  1  1 X^2+X  1  1
 0  1  0  1 X^2+X X^2+X+1  1  0 X^2
 0  0  1  1 X+1  X X+1 X+1 X^2
 0  0  0 X^2  0  0 X^2 X^2 X^2

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+41x^6+132x^7+149x^8+388x^9+150x^10+108x^11+42x^12+12x^13+1x^14

The gray image is a linear code over GF(2) with n=36, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00237 seconds.